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2018-2019 Academic Catalog [ARCHIVED CATALOG]
Mathematics Courses
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Mathematics and Statistics
Mathematics and Statistics
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MAT 115 - Introduction to Statistics 4 credits (Fall and Spring)
Cross-listed as: SST 115 . Introduces the notions of variability and uncertainty and such common statistical concepts as point and interval estimation and hypothesis testing. Data-oriented, with real-world examples chosen from the social and biological sciences. The computer is used for data analysis and to illustrate probabilistic and statistical concepts. A student who takes MAT-115 cannot receive credit for STA 209 .
Prerequisite: Two years of high school algebra and second semester of first-year standing.
Instructor: Staff -
MAT 123 - Functions and Differential Calculus 4 credits (Fall)
An introductory course in mathematics and the first in a two-course sequence. This first semester is an introduction to the differential calculus of functions of one variable with an extensive review of precalculus topics such as algebra and functions. This review, together with an emphasis on developing problem-solving skills, is designed to help students learn to do mathematics at the college level. MAT 123-MAT 124 has the same calculus content as MAT 131 .
Prerequisite: Two years of high school algebra.
Instructor: Staff -
MAT 124 - Functions and Integral Calculus 4 credits (Spring)
A continuation of MAT 123 . An introduction to the integral calculus of functions of one variable. Topics include the definite integral, techniques of integration, and applications of the integral. Successful completion of this course prepares students for MAT 133 .
Prerequisite: MAT 123 .
Instructor: Staff -
MAT 131 - Calculus I 4 credits (Fall)
The first in a two-course sequence. An introduction to the differential and integral calculus of functions of one variable. Also introduces a few concepts and methods of differential equations.
Prerequisite: Good preparation, including trigonometry, or departmental placement.
Instructor: Staff -
MAT 133 - Calculus II 4 credits (Fall and Spring)
A continuation of MAT 131 . Topics include functions of more than one variable: partial and total derivatives, multiple integrals, vector-valued functions, and parametrized curves. Additional topics may include applications to differential equations, line integrals, and Green’s Theorem.
Prerequisite: Mathematics MAT 124 or MAT 131 .
Instructor: Staff -
MAT 208 - Discrete Structures 4 credits (Spring)
See CSC 208 .
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MAT 215 - Linear Algebra 4 credits (Fall and Spring)
A unified study of the concepts underlying linear systems and linear transformations and of the techniques for using them. Topics: matrix algebra, rank, orthogonality, vector spaces and dimension, eigenvectors and eigenvalues. Typical applications: fitting lines and curves to data, Markov processes, linear differential equations.
Prerequisite: MAT 133 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 218 - Discrete Bridges to Advanced Mathematics 4 credits (Fall and Spring)
Discrete Bridges to Advanced Mathematics courses prepare students for the 300-level foundations courses through careful attention to mathematical proof writing and creative problem solving. Skill building is a fundamental component: skills include working with fundamental tools of logic to write convincing arguments, grappling deeply with difficult mathematical problems, and reading upper-level undergraduate mathematical texts. Math 218 addresses counting techniques and other discrete topics needed for computer science. May be repeated once for credit when content changes with permission of instructor. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 215 .
Instructor: Staff -
MAT 220 - Differential Equations 4 credits (Spring)
First and second order differential equations; series solutions and Fourier series; linear and nonlinear systems of differential equations; applications.
Prerequisite: MAT 215 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 222 - Bridges to Advanced Mathematics 4 credits (Fall or Spring)
Bridges to Advanced Mathematics courses prepare students for 300-level foundations courses through careful attention to mathematical proof writing and creative problem solving. Skill building is a fundamental component: skills include working with fundamental tools of logic to write convincing arguments, grappling deeply with difficult mathematical problems, and reading upper-level undergraduate mathematics texts. May be repeated once for credit when content changes with permission of instructor. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 215 .
Instructor: Staff -
MAT 271 - Problem-Solving Seminar 1 credits (Fall)
Students solve challenging mathematics problems and present solutions. Prepares students to take the Putnam Examination, if they wish. May be repeated for credit.
Prerequisite or co-requisite: Completion of, or concurrent registration in
S/D/F only.
Instructor: Staff -
MAT 306 - Mathematical Modeling 4 credits (Spring)
An introduction to the process and techniques of modeling “real-world” situations, using topics from linear algebra and differential equations. Appropriate mathematics, including numerical methods, developed when needed. Models drawn from both the social and natural sciences.
Prerequisite: MAT 220 .
Note: Plus-2 option available. Not offered every year. Offered in alternate years.
Instructor: Staff -
MAT 314 - Topics in Applied Mathematics 4 credits (Spring)
Topics include, but are not limited to, one of the following: Chaos and Fractals (one- and two-dimensional discrete dynamics, iterated function systems, fractal dimension), Fourier Analysis (fast Fourier transform, Fourier series, wavelets), or Partial Differential Equations (heat and wave equation, eigenfunction expansions). May be repeated for credit when content changes. For current course content see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: Varies depending on topic.
Note: Plus-2 option available. Offered in alternate years.
Instructor: Staff -
MAT 316 - Foundations of Analysis 4 credits (Fall and Spring)
A thorough study of the topology of the real line and of limits of functions of one real variable. This theory is then used to develop the theory of the derivative and integral of functions of one real variable and also sequences and series of real numbers and functions.
Prerequisite: MAT 218 or MAT 222 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 317 - Advanced Topics in Analysis 4 credits (Fall)
Analysts seek to understand mathematical entities, such as numbers, vectors, and functions, through approximation, convergence, and representation. This approach has yielded important insights in pure mathematics, in areas like differential equations, geometry, and number theory, as well asapplications in areas like signal processing, data analysis, and quantum theory. This course will build on the foundations of analysis, exploring an advanced topic in this area. The course will regularly provide an opportunity to pursue research. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 316 .
Instructor: Staff -
MAT 321 - Foundations of Abstract Algebra 4 credits (Fall and Spring)
The study of algebraic structures, with emphasis on formal systems such as groups, rings, and fields.
Prerequisite: MAT 218 or MAT 222 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 322 - Advanced Topics in Algebra 4 credits (Spring)
Algebraists study sets with operations, such as matrices under addition and multiplication. Algebraic structures are central in modern mathematics, arising in areas like number theory and combinatorics, topology and geometry, and also finding applications in fields like cryptography and coding theory - even data analysis and music theory. This course will build on the foundations of abstract algebra, exploring an advanced topic in this area. The course will regularly provide an opportunity to pursue research. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 321 .
Instructor: Staff -
MAT 335 - Probability and Statistics I 4 credits (Fall)
Cross-listed as: STA 335 . An introduction to the mathematical theory of probability and statistical inference. Discrete and continuous distributions, as well as sampling distributions and the limit theorems of probability, will be introduced. The importance of randomization and simulation for computing statistical probabilities will be explored.
Prerequisite: MAT 215 ; and STA 209 (previously offered as MAT 209), MAT 218 , or MAT 220 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 336 - Probability and Statistics II 4 credits (Spring)
Cross-listed as: STA 336 . A systematic treatment of mathematical statistics based on probability theory. Topics will include: principles of estimation and hypothesis testing, chi-square tests, linear models including regression and analysis of variance, and nonparametric inference. A variety of applications will be considered.
Prerequisite: MAT 335 or STA 335 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 444 - Senior Seminar 4 credits (Spring)
Advanced course with varying content. Strongly recommended for students considering further work in mathematics and statistics. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: Will vary depending on topic.
Note: Plus-2 option available.
Instructor: Staff
Statistics
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STA 209 - Applied Statistics 4 credits (Fall and Spring)
The course covers the application of basic statistical methods such as univariate graphics and summary statistics, basic statistical inference for one and two samples, linear regression (simple and multiple), one- and two-way ANOVA, and categorical data analysis. Students use statistical software to analyze data and conduct simulations. A student who takes Statistics 209 cannot receive credit for MAT 115 or SST 115 .
Prerequisite: MAT 124 or MAT 131 .
Note: Plus-2 option available. Previously offered as MAT-209.
Instructor: Staff -
STA 309 - Design and Analysis of Experiments 4 credits (Spring)
In addition to a short review of hypothesis testing, confidence intervals, and 1-way ANOVA, this course incorporates experiments from several disciplines to explore design and analysis techniques. Topics include factorial designs, block designs (including latin square and split plot designs), random, fixed, and mixed effects models, crossed and nested factors, contrasts, checking assumptions, and proper analysis when assumptions are not met.
Prerequisite: STA 209 (previously offered as MAT-209), MAT 336 , or STA 336 .
Note: Plus-2 option available. Not offered every year. Offered in alternate years.
Instructor: Staff -
STA 310 - Statistical Modeling 4 credits (Fall)
This course will focus on investigative statistics labs emphasizing the process of data collection and data analysis relevant for science, social science, and mathematics students. This course incorporates case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include nonparametric tests, designing an experiment, and generalized linear models.
Prerequisite: STA 209 (previously offered as MAT 209), MAT 336 , or STA 336 .
Instructor: Staff -
STA 335 - Probability and Statistics I 4 credits (Fall)
See MAT 335 .
Variable Topics - Fall
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MAT 317-01 - Advanced Topics in Analysis: Experimental Analysis 4 credits (Fall)
The pure mathematician has traditionally solved problems by “paper and pencil.” While the use of computers has changed our world in many respects, this has not (with few exceptions) come back to help mathematicians in their research. This course will show how computers can be used to study problems connected to analysis, including problems with integrals, infinite series, difference equations, chaos theory, and root finding. The common thread is using the computer for discovery; symbolic, numerical and visual. Students will master a computer algebra system, learn some recently developed algorithmic tools, and work on a research project. Previous experience with a computer algebra system is not required.
Prerequisite: MAT 316 .
Instructor: Chamberland
Variable Topics- Spring
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MAT 218-01 - Discrete Bridges to Advanced Mathematics: Number Theory 4 credits (Spring)
Number theory is one of the oldest branches of mathematics, far older than Calculus. The subject, at its most basic, asks questions about the integers. For instance, how are the prime numbers distributed among the integers? What are integer solutions to a particular polynomial equation? Which integers can be expressed as the sum of two squares? We will learn about topics such as divisibility, congruences, and quadratic reciprocity, which will help us answer questions like these. Along the way, we will discuss counting techniques and related discrete topics. Proof writing and creative problem solving will be heavily emphasized.
Prerequisite: MAT 215 .
Instructor: Paulhus -
MAT 314-01 - Topics in Applied Mathematics: Partial Differential Equations 4 credits (Spring)
Partial Differential Equations. This is a first course in partial differential equations. The development of the theory and techniques will revolve around several classical equations: Laplace’s equation, the heat equation (heat flow and diffusion), and the wave equation. Techniques will include separation of variables, Fourier analysis, Sturm-Liouville problems, and existence/uniqueness results.
Prerequisite: MAT 220 .
Instructor: Chamberland -
MAT 322-01 - Advanced Topics in Algebra: Elliptic Curves 4 credits (Spring)
Elliptic curves play a crucial role in modern mathematics from pure mathematics (the proof of Fermat’s Last Theorem) to applied mathematics (elliptic-curve cryptography). These surprisingly sophisticated objects are solutions to cubic equations. To be able to understand how these curves are used, we need to develop their algebraic properties, particularly a beautiful group structure we can create on the solutions. There will be a research component to the class.
Prerequisite: MAT 321 .
Instructor: Paulhus -
MAT 444-01 - Senior Seminar: Geometric Group Theory 4 credits (Spring)
Despite its role as a cornerstone of abstract algebra, group theory is an intrinsically geometric subject. From the work of Klein in the late 19th century to Gromov’s foundational results nearly a century later, geometry has proven to be a powerful tool and a natural way to understand groups. The connections between these two areas, together with subjects such as topology, combinatorics, and formal language theory, form the basis for the field known as geometric group theory.
In this course we will take an in-depth tour of several topics in geometric group theory, focusing especially on the interactions between groups and graphs. As part of the course, students will have the opportunity to complete a research project which explores a chosen topic in detail, including its relevance to geometric group theory and neighboring fields.
Prerequisite: MAT 321 . Recommended - MAT 316 . Exposure to combinatorics will be useful, but not required.
Instructor: Dougherty
Variable Topics - Fall and Spring
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MAT 218-01 & 02 - Discrete Bridges to Advanced Mathematics: Graph Theory 4 credits (Fall and Spring)
A graph consists of a set of vertices and a set of edges - you can draw a graph simply by placing some dots on a page to represent vertices, and then connecting certain pairs of dots with lines to represent the edges. Graphs are useful for understanding any kind of networks - the internet itself could be viewed as a graph, with links between pages representing edges; in fact Google’s PageRank algorithm makes heavy use of ideas from graph theory. In this course, we will use graphs as a means to develop problem solving skills and to improve our ability to construct logical mathematical arguments. After beginning with basic topics including the chromatic number, planarity, trees, Euler circuits, and Hamiltonian cycles.
Prerequisite: MAT 215 .
Note: Fall: Sections 01 & 02. Spring: Section 02
Instructor: Uzzell
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